Multiplying Decimals
What Is This?
Multiplying decimals follows the same process as multiplying whole numbers — with one extra step at the end: counting decimal places to position the decimal point in the answer. You do not need to line up decimal points the way you do when adding or subtracting. Instead, you ignore the decimal points during multiplication, then place the decimal point in the correct position once you have your answer.
Why Does It Matter?
Every time you scale a measurement, calculate a price, or work with rates, you are multiplying decimals. Finding the cost of 3.5 metres of fabric, calculating 1.5 times a recipe, or converting units all require this skill. Multiplying decimals also underpins area calculations and percentage problems at higher grades.
The Core Rule — Count Decimal Places
The number of decimal places in the answer equals the total number of decimal places in both factors combined.
| Factor 1 | Factor 2 | Total decimal places | Answer |
|---|---|---|---|
| 0.3 (1 d.p.) | 4 (0 d.p.) | 1 | 1.2 |
| 0.6 (1 d.p.) | 0.5 (1 d.p.) | 2 | 0.30 |
| 2.4 (1 d.p.) | 1.3 (1 d.p.) | 2 | 3.12 |
| 0.25 (2 d.p.) | 0.4 (1 d.p.) | 3 | 0.100 |
Method 1 — Multiplying a Decimal by a Whole Number
Example: 3.4 × 6
Step 1: Ignore the decimal point and multiply as whole numbers.
- 34 × 6 = 204
Step 2: Count the decimal places in the original problem.
- 3.4 has 1 decimal place; 6 has 0.
- Total = 1 decimal place.
Step 3: Place the decimal point 1 place from the right of your answer.
- 204 → 20.4
Answer: 20.4 ✓
Method 2 — Multiplying a Decimal by a Decimal
Example: 2.4 × 1.3
Step 1: Multiply as whole numbers.
- 24 × 13 = 312
Step 2: Count total decimal places.
- 2.4 has 1; 1.3 has 1. Total = 2.
Step 3: Place the decimal point 2 places from the right.
- 312 → 3.12
Answer: 3.12 ✓
Multiplying by 0.1 and 0.01
Multiplying by 0.1 is the same as dividing by 10 — move the decimal point one place to the left. Multiplying by 0.01 is the same as dividing by 100 — move the decimal point two places to the left.
| Expression | Answer |
|---|---|
| 7 × 0.1 | 0.7 |
| 45 × 0.1 | 4.5 |
| 6 × 0.01 | 0.06 |
| 3.8 × 0.1 | 0.38 |
Worked Examples
Worked Example 1: 0.6 × 0.5
- Whole number product: 6 × 5 = 30
- Decimal places: 1 + 1 = 2
- Place decimal: 30 → 0.30 = 0.30
Note: The leading zero is needed because there are no ones — the answer is 30 hundredths.
Worked Example 2: 4.25 × 3
- Whole number product: 425 × 3 = 1275
- Decimal places: 2 + 0 = 2
- Place decimal: 1275 → 12.75
Worked Example 3: 1.2 × 1.5
- Whole number product: 12 × 15 = 180
- Decimal places: 1 + 1 = 2
- Place decimal: 180 → 1.80 = 1.8
Worked Example 4: 0.4 × 0.25
- Whole number product: 4 × 25 = 100
- Decimal places: 1 + 2 = 3
- Place decimal: 100 → 0.100 = 0.1
Note: Count from the right — 3 places in 100 gives 0.100. The trailing zeros can be dropped: 0.1.
Worked Example 5 (Word Problem): A ribbon costs $2.35 per metre. How much do 4 metres cost?
- 2.35 × 4
- Whole number: 235 × 4 = 940
- Decimal places: 2
- Answer: 940 → $9.40
Estimating to Check
Round each factor to the nearest whole number before multiplying. If your exact answer is far from the estimate, recheck your decimal placement.
Example: 3.7 × 4.2
- Estimate: 4 × 4 = 16
- Exact: 37 × 42 = 1554 → 2 decimal places → 15.54 ✓ (close to 16)
Common Mistakes
Mistake 1: Lining up decimal points Decimal points do NOT need to be aligned when multiplying. Alignment is only for addition and subtraction.
Mistake 2: Counting decimal places wrong Always count the total decimal places across BOTH factors. For 2.4 × 1.3, that is 1 + 1 = 2, not 1.
Mistake 3: Forgetting the leading zero 0.6 × 0.5 = 0.30, not .30 or 30. When the answer is less than 1, always write a zero before the decimal point.
Mistake 4: Not enough digits for decimal placement If the whole-number product has fewer digits than the number of decimal places, pad with leading zeros. Example: 0.3 × 0.2 → 3 × 2 = 6 → 2 decimal places → 0.06 (not 0.6).
Key Takeaways
- Multiply as if the decimal points are not there, then place the decimal point at the end
- The answer has as many decimal places as the two factors combined
- Multiplying by 0.1 moves the decimal one place left; multiplying by 0.01 moves it two places left
- Estimate first to check your answer is reasonable
- When the product is less than 1, write a leading zero before the decimal point
- Pad with leading zeros if the whole-number product doesn't have enough digits
Practice and Resources
Ready to practise? Try our Grade 3-5 Multiplying Decimals Worksheet covering whole number × decimal, decimal × decimal, and word problems. Test yourself with the Grade 3-5 Math Practice Test.